Chains of Rydberg atoms have emerged as an amazing playground to study quantum physics in 1D. Playing with inter-atomic distances and laser detuning, one can in particular explore the commensurate-incommensurate transition out of density waves through the Kibble-Zurek mechanism, and the possible presence of a chiral transition with dynamical exponent z>1. Here, we address this problem theoretically with effective blockade models where the short-distance repulsions are replaced by a constraint of no double occupancy. For the period-4 phase, we show that there is an Ashkin-Teller transition point with exponent nu=0.78 surrounded by a direct chiral transition with a dynamical exponent z=1.11 and a Kibble-Zurek exponent mu=0.41. For Rydberg atoms with a van der Waals potential, we suggest that the experimental value mu=0.25 is due to a chiral transition with z similar or equal to 1.9 and nu similar or equal to 0.47 surrounding an Ashkin-Teller transition close to the 4-state Potts universality. Phase transition occurring in quantum material is an intriguing phenomenon. Here, the authors discuss the commensurate-incommensurate phase transition out of the period-4 phase on a chain of Rydberg atoms and emphasize the emergence of a chiral transition.